Solve for $x$ and $y$ using elimination. ${-3x-3y = -30}$ ${3x+2y = 21}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3x$ and $3x$ cancel out. $-y = -9$ $\dfrac{-y}{{-1}} = \dfrac{-9}{{-1}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {-3x-3y = -30}\thinspace$ to find $x$ ${-3x - 3}{(9)}{= -30}$ $-3x-27 = -30$ $-3x-27{+27} = -30{+27}$ $-3x = -3$ $\dfrac{-3x}{{-3}} = \dfrac{-3}{{-3}}$ ${x = 1}$ You can also plug ${y = 9}$ into $\thinspace {3x+2y = 21}\thinspace$ and get the same answer for $x$ : ${3x + 2}{(9)}{= 21}$ ${x = 1}$